The Very General Verra Fourfold is Irrational
Algebraic Geometry
2026-04-17 v1
Abstract
We show that the very general Verra fourfold is irrational, using the Hodge atom framework of Katzarkov--Kontsevich--Pantev--Yu. Two novel points are: a refined analysis of Hodge atoms, based on the involution on the cohomology of , and a derivation of the quantum multiplication matrix from the quantum differential operator. This gives the first successful application of the method of Hodge atoms to a space with Picard rank greater than one.
Keywords
Cite
@article{arxiv.2604.14850,
title = {The Very General Verra Fourfold is Irrational},
author = {Aideen Fay},
journal= {arXiv preprint arXiv:2604.14850},
year = {2026}
}